In this paper we consider Z-actions, d ≥ 1, by automorphisms of compact connected abelian groups which contain at least one expansive automorphism (such actions are called algebraic Z-actions of expansive rank one). If α is such a Z-action on an infinite compact connected abelian group X, then every expansive element α of this action has a dense group ∆αn(X) of homoclinic points. For different ...

This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (R, ‖ · ‖) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f : X → X , converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm,...

A class of data-reusing learning algorithms for real-time recurrent neural networks (RNNs) is analyzed. The analysis is undertaken for a general sigmoid nonlinear activation function of a neuron for the real time recurrent learning training algorithm. Error bounds and convergence conditions for such data-reusing algorithms are provided for both contractive and expansive activation functions. Th...

Introduction the expansive soil shows obvious volumetric changes under changing moisture conditions. these volumetric deformations usually result in differential movements of shallow foundations resting on it. consequently, structural damages could happen if no special measures would have been taken during the design process. this article illustrates the possibility to predict such movements us...